Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids
The main purpose of the paper is the presentation of a new central essentially nonoscillatory (ENO) scheme, which is of third order and does not require field-by-field decomposition. First, the standard ENO schemes developed by \textit{C.-W. Shu} and \textit{S. Osher} [J. Comput. Phys. 83, No.~1, 32-78 (1989; Zbl 0674.65061)] are revisited by using point values instead of cell averages, which avoids staggering, as well as component-wise limiting. Next the authors introduce a new type of decision process called ``convex ENO'', which yields the desired scheme. They insist on the fact that their flux does degenerate to first order at discontinuities. Furthermore, their scheme is easily extended to multi-dimensions. Numerical results are reported in detail for 10 significant test problems in one or two dimensions. They are excellent. It is also pointed out that the component-wise calculation is twice as fast as the field-by-field decomposition version of the scheme in each dimension.
scientific article; zbMATH DE number 1281849